8x+5=10/3x

Solution for 8x+5=10/3x equation:

8x+5=10/3x

We move all terms to the left:

8x+5-(10/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+10/3x)+5=0

We get rid of parentheses

8x-10/3x+5=0

We multiply all the terms by the denominator


8x*3x+5*3x-10=0

Wy multiply elements

24x^2+15x-10=0

a = 24; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·24·(-10)
Δ = 1185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{1185}}{2*24}=\frac{-15-\sqrt{1185}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{1185}}{2*24}=\frac{-15+\sqrt{1185}}{48}
$